nips nips2001 nips2001-21 nips2001-21-reference knowledge-graph by maker-knowledge-mining
Source: pdf
Author: Dörthe Malzahn, Manfred Opper
Abstract: We combine the replica approach from statistical physics with a variational approach to analyze learning curves analytically. We apply the method to Gaussian process regression. As a main result we derive approximative relations between empirical error measures, the generalization error and the posterior variance.
[1] N. Murata, S. Yoshizawa, S. Amari, IEEE Transactions on Neural Networks 5, p. 865-872, (1994).
[2] A. Engel, C. Van den Broeck, Statistical Mechanics of Learning, Cambridge University Press (2001).
[3] D. Malzahn, M. Opper, Neural Information Processing Systems 13, p. 273, T. K. Leen, T. G. Dietterich and V. Tresp, eds., MIT Press, Cambridge MA (2001).
[4] D. Malzahn, M. Opper, Lecture Notes in Computer Science 2130, p. 271, G. Dorffner, H. Bischof and K. Hornik, eds., Springer, Berlin (2001).
[5] M. M´ zard, G. Parisi, M. Virasoro, Spin Glass Theory and Beyond, World Scientific, e Singapore, (1987).
[6] R. P. Feynman and A. R. Hibbs, Quantum mechanics and path integrals, Mc GrawHill Inc., (1965).
[7] T. Garel, H. Orland, Europhys. Lett. 6, p. 307 (1988).
[8] P. Sollich, Neural Information Processing Systems 11, p. 344, M. S. Kearns, S. A. Solla and D. A. Cohn, eds., MIT Press, Cambridge MA (1999).
[9] P. Sollich, Neural Information Processing Systems 14, T. G. Dietterich, S. Becker, Z. Ghahramani, eds., MIT Press (2002).